Frequency selective devices, such as filters, pass signals of certain frequencies and attenuate signals of other frequencies. Many filter topologies require the use of resonant circuits comprising the parallel or series connection of transconductance amplifiers arranged in gyrator configurations, resistors, and capacitors on an integrated circuit. The resonant frequency .omega..sub.o is defined by the equation .omega..sub.o =g/C, where g is the transconductance of the amplifiers and C is the capacitance of the circuit. The center frequency of these circuits can be held constant over temperature by controlling the ratio of the amplifier transconductance to the nodal capacitance. Most forms of integrated capacitors have a low temperature coefficient, thus the problem is reduced to maintaining constant transconductance. For a typical transconductance amplifier, this can be achieved by making the bias current of the amplifier linearly dependent on temperature.
The quality factor (Q) of the resonant circuit refers to the energy stored in the circuit vs. the energy dissipated in the circuit, and, if the resonant frequency is held constant, the Q determines the bandwidth of the filter. The Q is defined by the equation Q=gR in a parallel resonant circuit and by the equation Q=1/gR in a series resonant circuit, where R refers to the resistance of the circuit. If the transconductance of the amplifiers is held constant, the Q may be controlled by holding the resistance constant over temperature. However, typical integrated circuit resistors of reasonable size have relatively large temperature coefficients. In some known filters, the resistors are approximated by the use of transconductance amplifiers whose bias current is made linearly dependent on temperature. Although these filters hold the Q constant over temperature, they require more current drain and additional components. Use of this type of filter might create a problem, for example, if battery life is of concern or if the space is at a premium in the component area.